The sum of three numbers is 1032. Find the numbers, knowing that the second number is three times the first number and the third number is 60 more than half of the first number.

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# 2 Answers

Given: a + b + c = 1032

Given: b = 3a

Given: c = a/2 + 60

Substitute: a + (3a) + (a/2 + 60) = 1032

Solve for a:

Combine like terms: 4a + a/2 + 60 = 1032

Subtract 60 from both sides: 4a + a/2 = 972

Multiply both sides by 2: 8a + a = 1944

Combine like terms: 9a = 1944

Divide both sides by 9: a = 216

a= 216

b = 3 * 216 = 648

c = (216/2) + 60 = 168

PROVE: 216 + 648 + 168 = 1032

Hi Sarah,

Let the three numbers be x, y and z

The sum of three numbers=1032

x+y+z=1032 equation 1

The second number is three times the first number

y=3x equation 2

The third number is 60 more than half of the first number

z=60+(1/2)x equation 3

substitute the values of y and z in equation 1

x+3x+60+(1/2)x=1032

(9/2)x=1032-60

(9/2)x=972

x=(972)(2/9)

x=216

substitute the value of x in equation 2

y=3x

y=3(216)=648

substitute the value of x in equation 3

z=60+(1/2)x

z=60+(1/2)(216)

=60+108

=168

so the answer is x=216, y=648 and z=168